Performance analysis of spectrum sensing schemes based on fractional lower order moments for cognitive radios in symmetric α-stable noise environments

Spectrum sensing schemes based on fractional lower order moment (FLOM) are often used in impulsive noise environments in which traditional energy detectors are not applicable. The performance of FLOM-based detectors operating in an α-stable noise environment is difficult to evaluate. This is because α-stable random variables can usually only be modeled by the characteristic function since closed-form expressions are not available, except for the special values of the characteristic exponent that correspond to the Cauchy and Gaussian noise distributions. In this paper, we derive closed-form expressions for the probability density function (PDF) and corresponding complementary cumulative distribution function (CDF) for a symmetric α-stable random variable with an arbitrary characteristic exponent α (0 < α ≤ 2) in terms of the Meijer G-function. Consequently, we evaluate the receiver operating characteristics (ROC) curve for the FLOM detectors. The analytical results are validated with Monte Carlo simulations.